CN103559414B - A kind of envirment factor the point estimation method based on Arrhenius relationship - Google Patents

Abstract

The invention discloses a kind of envirment factor the point estimation method based on Arrhenius relationship, pass through Performance Degradation Data, draw Degradation path, set inefficacy threshold values, pseudo-burn-out life data are obtained further according to degradation model, after the distribution of the pseudo-burn-out life data of checking, using the pseudo-burn-out life data obtained as non-fully sample, get truncated sample.According to envirment factor for the concrete definition being distributed, provide the expression formula of envirment factor based on Arrhenius relationship, and estimate the parameter in envirment factor expression formula by the optimum linear estimation technique, finally verify calculated envirment factor, the reliability estimation so making product is more accurate, has the performance of high efficiency, low cost simultaneously.

Description

Environmental factor point estimation method based on Arrhenius model

Technical Field

The invention belongs to the technical field of service life prediction and reliability prediction of products, and particularly relates to an environment factor point estimation method based on an Arrhenius model.

Background

In the reliability evaluation of products, tests are often performed in a plurality of environments to acquire performance data of products running under different environmental conditions, but due to the limitation of conditions, data acquisition under actual working environmental conditions is difficult, and test data and information under severe environments can be converted into test data which needs to be acquired under actual conditions through environmental factors, so that the test cost is reduced, the sample capacity is expanded, and the reliability is improved.

The environmental factor is used as a conversion factor, mainly converts failure life data in one environment into failure life data in another environment, represents the failure speed of the same product in different environments, and reflects the severe level of the influence of the environment on the reliability of the product. The traditional environmental factor is subjected to statistical inference based on a large amount of failure life data, and after improvement, the environmental factor can be evaluated based on the failure life data of a small sample by utilizing prior information. In the article 'environmental factor estimation theory and application thereof in reliability evaluation' of Lifeng, Bayesian theory is used to fully utilize the characteristics of prior information, Bayes point estimation of several commonly distributed environmental factors under small characters is researched, but the environmental factors are estimated based on failure life data.

In the existing documents, after an expression of environment factor point estimation is given, the calculation results are compared through calculating the mean square error, the maximum likelihood estimation and the Bayes estimation of the gamma distribution environment factors are given in 'the maximum likelihood estimation and the Bayes estimation of the gamma distribution environment factors' by the Sasa and the like based on failure life data, and the mean square error of the two methods is calculated through numerical simulation to show that the Bayes estimation is superior to the maximum likelihood estimation. The disadvantage is that, in the absence of sufficient test data, data can only be obtained by numerical simulation, and the calculation process is complicated and the results obtained are also inaccurate.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides an environment factor point estimation method based on an Arrhenius model, so that the reliability of a product is more accurately estimated, and the method has the performances of high efficiency and low cost.

In order to achieve the above object, the method for estimating environmental factor points based on an arrhenius model of the present invention is characterized by comprising the following steps:

(1) calculating the pseudo-failure life data:

extracting samples from a product to be tested, drawing a degradation track according to degradation data of the samples, and collecting the ith sample at t_i1,t_i2...t_ijAmount of degradation y of each time point_ijGeneral model Y by Performance degradation analysis_ij＝D_ij+_ijI 1,2, n, j 1,2, i, l, a degradation trajectory D is fitted_ij＝D(t_ij,β_i) And estimating the parameters β by using a least square method_iWhere there are n samples, l observation time points,_ijis a random error, β_iIs the coefficient of the degraded trajectory equation of the i-th sample, y_ijIs the performance degradation amount of the ith sample at the jth observation time point, and sets a failure threshold value D_fLet y_ij＝D_fCalculating the time t for the sample to reach the failure threshold_ijObtaining the false failure life data of the sample;

(2) verifying the distribution of the false failure life data:

under S temperature stresses, n samples are in total under each temperature stress, the degradation amount of the samples under each temperature stress obeys the Weber distribution, the distribution parameters at different moments under each temperature stress are estimated, and then whether the shape parameters m are equal under each temperature stress is checked, namely m is₁＝m₂＝...＝m_k,k＝1,2,...S；

(3) Acquiring a truncation sample:

at a specific temperature T_kPseudo-failure life of the lower i-th sampleHandleRegarding as a non-complete sample, the temperature T_kThe pseudo-failure lifetimes of the following n samples are ranked from small to large:at a temperature T_kTaking r truncated data from the n samples as truncated samples, namely taking the truncated data r as n;

(4) acquiring an environment factor expression based on an Arrhenius model, and calculating parameters in the expression:

the linearized expression of the arrhenius model is:

lnL＝A+B/T_k

wherein A and B are parameters to be determined, L is life characteristic, and T_kIs the temperature;

according to the definition of the environmental factor, under two different environments, the ratio of the average life of the sample is the environmental factor, and then the environmental factor is expressed by the formula:

$K=\frac{L_1}{L_2}$

wherein K represents an environmental factor, L₁、L₂Indicating life characteristics at two different temperatures;

the temperature T is calculated at a characteristic lifetime of η for the Weber distribution_a,a∈[1,S]With respect to temperature T_b,b∈[1,S]The expression is as follows:

$K=\frac{{\mathrm{\η}}_1}{{\mathrm{\η}}_2}$

η₁represents the temperature T_aCharacteristic life of η₂Represents the temperature T_bCharacteristic life of the following; the lifetime-stress model under the weber distribution is then:

lnη＝A+B/T_k

at a temperature T_aAnd T_bThe lifetime-stress model under the weber distribution is:

lnη₁＝A+B/T_a

lnη₂＝A+B/T_b

then the environment factor expression based on the arrhenius model is:

$K=\frac{{\mathrm{\η}}_1}{{\mathrm{\η}}_2}=\frac{e^{A+B/T_a}}{e^{A+B/T_b}}=e^{B\[1/T_a-1/T_b\]}$

the best linear unbiased estimates of variance and mean derived from markov's theorem are:

${\widehat{\mathrm{\σ}}}_k=\underset{i=1}{\overset{r_k}{\Σ}}C(n_k,r_k,i){\mathrm{lnt}}_{ki},{\widehat{\mathrm{\μ}}}_k=\underset{i=1}{\overset{r_k}{\Σ}}D(n_k,r_k,i){\mathrm{lnt}}_{ki};$

the best linear unbiased estimate BLUE of A, B under a Weber distribution obtained by the Gaussian-Markov theorem is:

$\hat{A}=\frac{GH-IM}{EG-I^2},\hat{B}=\frac{EM-IH}{EG-I^2};$

wherein,

wherein, C (n)_k,r_kI) and D (n)_k,r_kI) called BLUE coefficient, n_k,r_kRespectively, the stress at temperature T_kLower, n_kTaking out of each sample_kA number of fixed number of truncated samples,is composed of a sample t_kiBy passingCalculating the obtained function;

(5) verifying the obtained environmental factors:

the environmental factor is verified by a ratio based on the sample performance degradation rate under two temperature stresses, and the method comprises the following steps:

after the time t passes, the sample generates a cumulative degradation amount M, and the performance degradation rate I is:

$I=\frac{M}{t}$

at a temperature T_aIf M is₁Is the amount of degradation of the initial state, M₂The degradation amount of the state at the time of failure corresponds to the degradation time t₂-t₁Is the life characteristic L of the sample₁The degradation rate I of the sample₁Comprises the following steps:

$\frac{M_2-M_1}{t_2-t_1}$

at a temperature T_bIf M is₃Is the amount of degradation of the initial state, M₄The degradation amount of the state at the time of failure corresponds to the degradation time t₄-t₃Is the life characteristic L of the sample₂The degradation rate I of the sample₂Comprises the following steps:

$\frac{M_4-M_3}{t_4-t_3}$

premise equivalent converted from environmental factors: at different temperatures T_a、T_bNext, the samples are each subjected to a time (t)₂-t₁)、(t₄-t₃) The amount of retrogradation was the same, i.e.: Δ M ═ M₂-M₁＝M₄-M₃，

$\frac{I_1}{I_2}=\left(\frac{M_2-M_1}{t_2-t_1}\right)/\left(\frac{M_4-M_3}{t_4-t_3}\right)=\frac{t_4-t_3}{t_2-t_1}=\frac{L_2}{L_1}$

Wherein, I₁Is T_aRate of deterioration of₂Is T_bThe degradation rate of the following, the environmental factor equivalent, is expressed as:

and (3) obtaining an environmental factor by estimating the ratio of the characteristic parameters under two temperature stresses, converting the degradation rate of the performance degradation data under one stress into the degradation rate under the other stress by using the environmental factor, and comparing the degradation rate with the value of the original degradation data under the other stress to verify the quality of an estimation result.

Wherein the degradation track D (t)_ij,β_i) The slope of (a) is the degradation rate of the sample being measured. The amount of degradation also follows a normal distribution.

The invention aims to realize the following steps:

according to the method for estimating the environmental factor points based on the Arrhenius model, the degradation track is drawn through the performance degradation data of the test sample, the degradation track is fitted according to the degradation model, the false failure life data is obtained through setting the failure threshold value, and the environmental factor is estimated based on the false failure life, so that the test time is greatly saved, the test efficiency is improved, and the test cost is reduced. According to the definition formula of the environment factors, an environment factor expression based on an Arrhenius model is given, parameters in the environment factor expression are estimated by using an optimal linear estimation method, and finally the calculated environment factors are verified, so that the reliability of the sample is estimated more accurately, and the workload is reduced.

Meanwhile, the method for estimating the environmental factor points based on the Allen model further has the following beneficial effects:

(1) the pseudo-failure life of the sample is estimated through the performance degradation data, and the environmental factor is estimated based on the pseudo-failure life, so that a large amount of real failure life data do not need to be collected, the requirement on the data for estimating the environmental factor is lower, the acquisition is easier, the operability of the test is improved, the test cost is greatly reduced, the test time is saved, and the test efficiency is improved.

(2) The performance degradation track of the sample after the environmental factor is converted is made by using a result verification method based on the graph, the conversion effect of the environmental factor is judged according to the relative position of the track, the degradation data is directly expressed through the degradation track without complex calculation, the target degradation track is obtained through the conversion of the environmental factor, the calculation result is visually displayed through the graph, the degradation trend of the sample can be seen, the influence of different environmental stresses on the performance of the sample can be visually seen, and the workload is greatly reduced.

Drawings

FIG. 1 is a flow chart of an embodiment of the method for estimating environmental factor points based on an Arrhenius model according to the present invention;

table 1 is a data record table for the test samples;

fig. 2 is a planar degradation trace plot of a test sample.

Detailed Description

The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.

Examples

FIG. 1 is a flow chart of an embodiment of the method for estimating environmental factor points based on an Arrhenius model according to the present invention;

in this embodiment, as shown in fig. 1, the method for estimating an environmental factor point based on an arrhenius model of the present invention includes the following steps:

s101, extracting a proper amount of carbon film resistors to serve as a detected sample, and acquiring degradation data of the sample;

s102, drawing a plane degradation track according to the degradation data of the samples, and collecting the ith sample at t_i1,t_i2...t_ijAmount of degradation y of each time point_ijGeneral model Y by Performance degradation analysis_ij＝D_ij+_ijI 1,2, n, j 1,2, i, l, a degradation trajectory D is fitted_ij＝D(t_ij,β_i) And adopt a minimum of twoMultiplicative estimation parameters β_iWhere there are n samples, l observation time points,_ijis a random error, β_iIs the coefficient of the degraded trajectory equation of the i-th sample, y_ijIs the amount of performance degradation at the point of time of the ith sample at the jth observation;

s103, setting a failure threshold value D_fLet y_ij＝D_fCalculating the time t for the sample to reach the failure threshold_ijObtaining the false failure life data of the sample;

s104, verifying the distribution of the pseudo-failure life data: under S temperature stresses, n samples are provided under each temperature stress, the degradation amount of the samples under each temperature stress obeys Weber distribution, distribution parameters at different moments under each temperature stress are estimated, whether the shape parameters m are equal under each temperature stress is checked, if yes, the step S105 is executed, and if not, the step S101 is executed again;

s105, at a specific temperature T_kPseudo-failure life of the lower i-th sampleHandleRegarding as a non-complete sample, the temperature T_kThe pseudo-failure lifetimes of the following n samples are ranked from small to large:at a temperature T_kTaking r truncated data from the n samples as truncated samples, namely taking the truncated data r as n;

s106, obtaining an environment factor expression based on an Arrhenius model: the linearized expression of the arrhenius model is:

lnL＝A+B/T_k

wherein A and B are parameters to be determined, L is life characteristic, and T_kIs the temperature;

according to the definition of the environmental factor, under two different environments, the ratio of the average life of the sample is the environmental factor, and then the environmental factor is expressed by the formula:

$K=\frac{L_1}{L_2}$

wherein K represents an environmental factor, L₁、L₂Indicating life characteristics at two different temperatures;

the temperature T is calculated at a characteristic lifetime of η for the Weber distribution_a,a∈[1,S]With respect to temperature T_b,b∈[1,S]The expression is as follows:

$K=\frac{{\mathrm{\η}}_1}{{\mathrm{\η}}_2}$

η₁represents the temperature T_aCharacteristic life of η₂Represents the temperature T_bCharacteristic life of the following; the lifetime-stress model under the weber distribution is then:

lnη＝A+B/T_k

at a temperature T_aAnd T_bThe lifetime-stress model under the weber distribution is:

lnη₁＝A+B/T_a

lnη₂＝A+B/T_b

then the environment factor expression based on the arrhenius model is:

$K=\frac{{\mathrm{\η}}_1}{{\mathrm{\η}}_2}=\frac{e^{A+B/T_a}}{e^{A+B/T_b}}=e^{B\[1/T_a-1/T_b\]}$

s107, calculating parameters A and B: the best linear unbiased estimates of variance and mean derived from markov's theorem are:

$\widehat{\mathrm{\σ}}k=\underset{i=1}{\overset{r_k}{\Σ}}C(n_k,r_k,i){\mathrm{lnt}}_{ki},{\widehat{\mathrm{\μ}}}_k=\underset{i=1}{\overset{r_k}{\Σ}}D(n_k,r_k,i){\mathrm{lnt}}_{ki};$

the best linear unbiased estimate BLUE of A, B under a Weber distribution obtained by the Gaussian-Markov theorem is:

$\hat{A}=\frac{GH-IM}{EG-I^2},\hat{B}=\frac{EM-IH}{EG-I^2};$

wherein,

wherein, C (n)_k,r_kI) and D (n)_k,r_kI) called BLUE coefficient, n_k,r_kRespectively, the stress at temperature T_kLower, n_kTaking out of each sample_kA number of fixed number of truncated samples,is composed of a sample t_kiA function obtained by calculation;

s108, verifying the obtained environmental factors:

after the time t passes, the sample generates a cumulative degradation amount M, and the performance degradation rate I is:

$I=\frac{M}{t}$

at a temperature T_aIf M is₁Is the amount of degradation of the initial state, M₂The degradation amount of the state at the time of failure corresponds to the degradation time t₂-t₁Is the life characteristic L of the sample₁The degradation rate I of the sample₁Comprises the following steps:

$\frac{M_2-M_1}{t_2-t_1}$

at a temperature T_bIf M is₃Is the amount of degradation of the initial state, M₄The degradation amount of the state at the time of failure corresponds to the degradation time t₄-t₃Is the life characteristic L of the sample₂The degradation rate I of the sample₂Comprises the following steps:

$\frac{M_4-M_3}{t_4-t_3}$

set at different temperatures T_a、T_bNext, the samples are each subjected to a time (t)₂-t₁)、(t₄-t₃) The amount of retrogradation was the same, i.e.: Δ M ═ M₂-M₁＝M₄-M₃Then the environment factor is equivalently expressed as:

the environmental factor K is estimated by the above method, comparison I₁And I₂If the two degradation tracks are parallel, the calculation value of the environmental factor meets the requirement, and if the two degradation tracks are not parallel, the calculation value of the environmental factor does not meet the requirement.

Table 1 is a data record table of the test samples.

In this embodiment, as shown in table 1, the carbon film resistor resistance values were subjected to performance degradation tests at three temperatures of 83 ℃, 133 ℃ and 173 ℃, the percentage increase of the resistance values with time was recorded, and the degradation was collected at four time points of 452h, 1030h, 4341h and 8084h, respectivelyData, assuming carbon film resistance failure threshold D_fIs 5, i.e. its resistance increases by 5%.

TABLE 1

Fig. 2 is a planar degradation trace plot of a test sample.

In this embodiment, the degradation trace is plotted based on the performance degradation data of the carbon film resistor recorded in table 1, and as shown in fig. 2, the degradation data of the carbon film resistor at 83 ℃, 133 ℃ and 173 ℃ are averaged, the degradation trace in which the degradation average of the carbon film resistor changes with time at each temperature is plotted, each degradation trace is seen as a nearly straight line, and the higher the temperature, the larger the slope of the degradation trace, and the faster the degradation rate. And then, the estimated environmental factor is used for converting the degradation track at other temperatures to 83 ℃, so that the slope of the degradation track of the carbon film resistor at 83 ℃ is unchanged, and the degradation tracks at 133 ℃ and 173 ℃ are parallel to the degradation track at 83 ℃, specifically, a dotted line in the figure when the degradation track is converted to 83 ℃ by the environmental factor. The product performance parameters at different temperatures have different degradation rates before the environmental factor is converted, and the degradation rates after the conversion are the same, so that the environmental factor obtained by the method has higher precision.

Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (3)

1. An environmental factor point estimation method based on an Arrhenius model is characterized by comprising the following steps:

(1) calculating the pseudo-failure life data:

extracting samples from a product to be tested, drawing a plane degradation track according to degradation data of the samples, and collecting the ith sample at t_i1,t_i2…t_ijAmount of degradation y of each time point_ijGeneral model Y by Performance degradation analysis_ij＝D_ij+_ijI 1,2, …, n, j 1,2, …, l, to fit the degradationTrack D_ij＝D(t_ij,β_i) And estimating the parameters β by using a least square method_iWhere there are n samples, l observation time points,_ijis a random error, β_iIs the coefficient of the degraded trajectory equation of the i-th sample, y_ijIs the performance degradation amount of the ith sample at the jth observation time point, and sets a failure threshold value D_fLet y_ij＝D_fCalculating the time t for the sample to reach the failure threshold_ijObtaining the false failure life data of the sample;

(2) verifying the distribution of the false failure life data:

under S temperature stresses, n samples are in total under each temperature stress, the degradation amount of the samples under each temperature stress obeys the Weber distribution, the distribution parameters at different moments under each temperature stress are estimated, and then whether the shape parameters m are equal under each temperature stress is checked, namely m is₁＝m₂＝…＝m_k,k＝1,2,…S；

(3) Acquiring a truncation sample:

at a specific temperature T_kPseudo-failure life of the lower i-th sampleHandleRegarding as a non-complete sample, the temperature T_kThe pseudo-failure lifetimes of the following n samples are ranked from small to large:at a temperature T_kTaking r truncated data from the n samples as truncated samples, namely taking the truncated data r as n;

(4) acquiring an environment factor expression based on an Arrhenius model, and calculating parameters in the expression:

the linearized expression of the arrhenius model is:

lnL＝A+B/T_k

wherein A and B are parameters to be determined, L is life characteristic,T_kis the temperature;

according to the definition of the environmental factor, under two different environments, the ratio of the average life of the sample is the environmental factor, and then the environmental factor is expressed by the formula:

$K=\frac{L_1}{L_2}$

wherein K represents an environmental factor, L₁、L₂Indicating life characteristics at two different temperatures;

the temperature T is calculated at a characteristic lifetime of η for the Weber distribution_a,a∈[1,S]With respect to temperature T_b,b∈[1,S]The expression is as follows:

$K=\frac{{\mathrm{\η}}_1}{{\mathrm{\η}}_2}$

η₁represents the temperature T_aCharacteristic life of η₂Represents the temperature T_bCharacteristic life of the following; the lifetime-stress model under the weber distribution is then:

lnη＝A+B/T_k

at a temperature T_aAnd T_bThe lifetime-stress model under the weber distribution is:

lnη₁＝A+B/T_a

lnη₂＝A+B/T_b

then the environment factor expression based on the arrhenius model is:

$K=\frac{{\mathrm{\η}}_1}{{\mathrm{\η}}_2}=\frac{e^{A+B/T_a}}{e^{A+B/T_b}}=e^{B\[1/T_a-1/T_b\]}$

the best linear unbiased estimates of variance and mean derived from markov's theorem are:

${\widehat{\mathrm{\σ}}}_k=\underset{i=1}{\overset{r_k}{\Σ}}C(n_k,r_k,i){\mathrm{lnt}}_{ki},{\widehat{\mathrm{\μ}}}_k=\underset{i=1}{\overset{r_k}{\Σ}}D(n_k,r_k,i){\mathrm{lnt}}_{ki};$

the best linear unbiased estimate BLUE of A, B under a Weber distribution obtained by the Gaussian-Markov theorem is:

$\hat{A}=\frac{GH-IM}{EG-I^2},\hat{B}=\frac{EM-IH}{EG-I^2};$

wherein,

wherein, C (n)_k,r_kI) and D (n)_k,r_kI) called BLUE coefficient, n_k,r_kRespectively, the stress at temperature T_kLower, n_kTaking out of each sample_kA number of fixed number of truncated samples,is composed of a sample t_kiA function obtained by calculation;

(5) verifying the obtained environmental factors:

the environmental factor is verified by a ratio based on the sample performance degradation rate under two temperature stresses, and the method comprises the following steps:

after the time t passes, the sample generates a cumulative degradation amount M, and the performance degradation rate I is:

$I=\frac{M}{t}$

at a temperature T_aIf M is₁Is the amount of degradation of the initial state, M₂The degradation amount of the state at the time of failure corresponds to the degradation time t₂-t₁Is the life characteristic L of the sample₁The degradation rate I of the sample₁Comprises the following steps:

$\frac{M_2-M_1}{t_2-t_1}$

at a temperature T_bIf M is₃Is the amount of degradation of the initial state, M₄Is lostThe degradation amount of the effective time state corresponds to the degradation time t₄-t₃Is the life characteristic L of the sample₂The degradation rate I of the sample₂Comprises the following steps:

$\frac{M_4-M_3}{t_4-t_3}$

premise equivalent converted from environmental factors: at different temperatures T_a、T_bNext, the samples are each subjected to a time (t)₂-t₁)、(t₄-t₃) The amount of retrogradation was the same, i.e.: Δ M ═ M₂-M₁＝M₄-M₃，

$\frac{I_1}{I_2}=\left(\frac{M_2-M_1}{t_2-t_1}\right)/\left(\frac{M_4-M_3}{t_4-t_3}\right)=\frac{t_4-t_3}{t_2-t_1}=\frac{L_2}{L_1}$

Wherein, I₁Is T_aRate of deterioration of₂Is T_bThe degradation rate of the following, the environmental factor equivalent, is expressed as:

and (3) obtaining an environmental factor by estimating the ratio of the characteristic parameters under two temperature stresses, converting the degradation rate of the performance degradation data under one stress into the degradation rate under the other stress by using the environmental factor, and comparing the degradation rate with the value of the original degradation data under the other stress to verify the quality of an estimation result.

2. The method of claim 1, wherein the degradation trajectory D (t) is a point of the environmental factor_ij,β_i) The slope of (a) is the degradation rate of the sample being measured.

3. The method of estimating environmental factor points based on an arrhenius model according to claim 1, wherein the amount of degradation is further subject to a normal distribution.